This iterative algorithm is also closely related to the Sinkhorn algorithm of Optimal Transport (OT).
In fact, Sinkhorn algorithm solves the entropy-regularized version of Optimal Transport [1]}.
However, our work concerns an different optimization instance. While OT solves a transportation problem where the solution space is defined with the marginal constraints over the rows and columns of a transportation matrix, our optimization problem is constrained with a total budget (\(\sum _i \lambda _i = k\) ) and upper bounds (\(\lambda _i \le 1\ \forall i\) ).
This leads to different iterative updates.
